Confinement and Mott transitions of dynamical charges in 1D lattice gauge theories

Lattice gauge theories (LGTs) have become a valuable tool to study strongly correlated condensed matter systems. This becomes in particular interesting when gauge degrees of freedom are coupled to matter since they allow us to study the complex problem of confinement. However, when the lattice is doped and matter becomes dynamical the clear notion of confinement becomes complicated. Here we study a one-dimensional (1D) Z₂ LGT model where the gauge fields are coupled to dynamical charges with confining Z₂ electric field and repulsive nearest-neighbour interactions. We map our model to a local string-length Hamiltonian where we link the confinement in the Z₂ LGT model to a broken translational symmetry in the string-length basis. In addition we study the Mott transition of the charges at a specific filling of n=2/3. We find that the metallic phase of the confined Luttinger liquid is characterized by a hidden off-diagonal quasi-long-range order. Furthermore we map the 1D Z₂ LGT model to a t-J_z model which can be implemented in cold atom experiments by using the Rydberg dressing schemes; thus, we propose a way to directly test our theoretical predictions.